The seriously ill baby boy was taken to hospital after being born at the Sports Direct distribution centre in Shirebrook, Derbyshire, on Wednesday.
Police said the woman arrested is thought to be the baby's mother, the BBC reported today.
A spokeswoman said the baby's condition has improved.
"A baby boy is being treated at a neonatal unit and is making good progress but is still undergoing tests," she said.
Police were called by the ambulance service at around midnight on January 1 to report the birth of the baby.
A spokesperson for Sports Direct declined to comment because of the police investigation and would not confirm if the mother was an employee.
Sports Direct has about 400 stores across the UK and describes itself as "the UK's leading sports retailer by revenue and operating profit".
It was founded by Mike Ashley, the billionaire owner of Newcastle United.
